# What is the period of f(t)=sin( (t)/2 )+ cos( (2t)/5 ) ?

$20 \pi$
Period of $\sin \left(\frac{t}{2}\right)$ --> $2 \left(2 \pi\right) = 4 \pi$
Period of cos $\left(\frac{2 t}{5}\right)$ --> $5 \frac{2 \pi}{2} = \frac{10 \pi}{2} = 5 \pi$
Period of f(t) --> least common multiple of $4 \pi$ and $5 \pi$ -->
$20 \pi$